Maricopa Project: Philosophy

Guiding Principles of the Maricopa Project

The pedagogical features provide a keen insight to the principles that guided the development of the Maricopa Mathematics Modules. Learning how the modules came to be reveals the background needs that led to writing the modules. We acknowledge the impact that many groups and individuals have had in rethinking foundation mathematics.

The Maricopa Mathematics Modules

These modules present mathematics to college students in fresh and engaging ways. The content is fresh; the pedagogical approach is engaging; the mathematical learning is powerful.

The modules can be configured into unique combinations to meet the needs of students in Foundation Mathematics (Arithmetic Review, Elementary and Intermediate Algebra), Quantitative Reasoning, Technical Mathematics or short courses. They can form the entire course, or they can be used as "replacement units" with more traditional texts. Each of the fifteen modules is approximately equal to a one-credit course.

Goal

Mathematics instruction at every level should propel students into future success as citizens, employees, employers, and as lifelong learners.

Philosophy

We believe that we should teach students what is most important. Therefore, we set our sights on six student outcomes that guide our work as authors and teachers. We believe that students should Connect, Reason, Express, Appreciate, Tap into technology and Establish a foundation as they develop their mathematical skills.

In order to achieve the CREATE outcomes, we believe that students need to gain a strong conceptual foundation of mathematics: that learning mathematics means to build strong connections among various topics of mathematics. We recognize that students do not build conceptual knowledge quickly, nor do they build a conceptual foundation by becoming proficient at doing template exercises and problems. Rather, students build conceptual knowledge by reflecting on their own knowledge and concepts.

To be successful in academic pursuits, as well as in life after college, students need to learn more mathematics than algebra. In the Maricopa Mathematics Modules, mathematical topics such as probability, sampling, geometry, and functions are interwoven with the development of algebra skills. In each module, students learn mathematics and mathematical language in a context of use. The mathematics in each module is grounded in the application of that mathematics. With the Maricopa Mathematics Modules, students do not wonder how this mathematics would ever be used.

We believe that all students can CREATE mathematics.

Pedagogical features

Activity-friendly

Each lesson is organized around student activities that are introduced by short expositions. Because the activities are part of the course material, it is easy to develop a classroom routine of active student involvement. Since students bring their own ideas and conjectures to the discussion, the whole class is enriched. Alternatively, some activities can be summarized by an interactive lecture; some activities can be done as homework. Most faculty teach the modules using a combination of lecture and collaborative groups.

Rule of 4

Students use four ways to express and explore mathematical ideas: graphically, numerically, symbolically, and verbally. In this way, students make a multitude of connections around specific mathematical concepts. For example, we ask them to tell the story that the function, P(x) = 1000(1.05)^x expresses. They should be able to create a meaningful context for the function, such as, "a population of 1000 grows by 5% per year." We ask them build a table of values for that function, to show its doubling time. We ask them to find the year when the population reaches 1750, by reading from a graph or by solving an equation using logarithms.

Technology

Students use graphing calculators daily throughout all the modules. Any graphing utility can be used, but it should have data lists, data plotting and regression capability. The features of the TI-83 calculator fit the material nicely. Since students use graphs and numerical exploration to learn the mathematics, they need ready access to this technology.

Nitty Gritty

The Nitty-Gritty feature focuses on specific skills. Nitty-Gritties appear intermittently, tied to the mathematics of a particular lesson. The Nitty-Gritty presents examples of a particular skill (as in solving an equation by taking the square root of both sides) followed by practice problems when it is important that students establish foundation skills.

Homework

The homework problems are designed to reinforce and extend the concepts of the lesson. They provide opportunities for problem solving. In the homework, students make progress toward accomplishment of the CREATE outcomes, as well as skill development. That is, the homework problems are not template problems. Each problem has a unique contribution to make to a student's gain in skills and understanding. Students should expect to do all of the homework problems.

Assessment

Most students appreciate the opportunity to show what they know in a variety of ways. For this reason we encourage a variety of assessments. In each lesson, students are encouraged to self-assess by completing the activities, the Wrap-Up boxes and the homework. Assessment ideas for instructors include quizzes, projects, research activities, writing assignments as well as tests.

How the Modules Came To Be

Many mathematics faculty acknowledge that mathematics courses at the foundation level are too tightly packed with a content that often seems disembodied. Students often fear this mathematics that seems irrelevant to their lives. Out of this realization, faculty in the Maricopa Community College District joined with their colleagues in area high schools and at Arizona State University to rethink the curriculum. Over 75 faculty participated at one time or another, over a period of about five years.

We wanted the mathematics experience of students to be rich in mathematics, not shallow in symbol manipulation skills. Therefore, we selected mathematics content that would prepare students for their further studies in economics, biology, physics, and accounting, for example, and not just the next mathematics course. We selected mathematics content that would prepare students for citizenship and lifelong learning.

As each module was conceptualized, student outcomes for that module were developed first. Then, the module was written. Modules have been class-tested, refined, reviewed, and class-tested again.

For more details, see the History pages.

Acknowledgments

The Maricopa Project wishes to thank the following for their unique contributions in bringing the Maricopa Project Modules to life, by their work in the Maricopa Mathematics Consortium (M²C):

• Thanks to the M²C Curriculum Team, who took the risk to rethink what students need to learn in mathematics, who devised a curriculum framework, and who developed student outcomes for the Project. Many different mathematics faculty accomplished this over a period of four years, from 1994 through 1997.
• Thanks to the M²C Assessment and Evaluation Team, who developed procedures and forms for formative evaluation of the modules, who took the risk to rethink how to evaluate an entire curriculum.

• Thanks to the 22 M²C writers, who gave form and life to the curriculum framework by creating the initial drafts and many subsequent revisions of the course material modules.

• Thanks to those who have class-tested the modules.

• Thanks to both math and non-math faculty who have reviewed the modules.

• Thanks to Dr. Alfredo G. de los Santos, Jr. for his generous support of mathematics reform in the Maricopa Community College District, and especially for his unwavering support of the effort which has resulted in the Maricopa Project modules.

Partial support for this work was provided by the National Science Foundation's Advanced Technological Education (ATE) Program through grant #DUE9602386. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect views of the National Science Foundation.

Activity-friendly	Each lesson is organized around student activities that are introduced by short expositions. Because the activities are part of the course material, it is easy to develop a classroom routine of active student involvement. Since students bring their own ideas and conjectures to the discussion, the whole class is enriched. Alternatively, some activities can be summarized by an interactive lecture; some activities can be done as homework. Most faculty teach the modules using a combination of lecture and collaborative groups.
Rule of 4	Students use four ways to express and explore mathematical ideas: graphically, numerically, symbolically, and verbally. In this way, students make a multitude of connections around specific mathematical concepts. For example, we ask them to tell the story that the function, P(x) = 1000(1.05)^x expresses. They should be able to create a meaningful context for the function, such as, "a population of 1000 grows by 5% per year." We ask them build a table of values for that function, to show its doubling time. We ask them to find the year when the population reaches 1750, by reading from a graph or by solving an equation using logarithms.
Technology	Students use graphing calculators daily throughout all the modules. Any graphing utility can be used, but it should have data lists, data plotting and regression capability. The features of the TI-83 calculator fit the material nicely. Since students use graphs and numerical exploration to learn the mathematics, they need ready access to this technology.
Nitty Gritty	The Nitty-Gritty feature focuses on specific skills. Nitty-Gritties appear intermittently, tied to the mathematics of a particular lesson. The Nitty-Gritty presents examples of a particular skill (as in solving an equation by taking the square root of both sides) followed by practice problems when it is important that students establish foundation skills.
Homework	The homework problems are designed to reinforce and extend the concepts of the lesson. They provide opportunities for problem solving. In the homework, students make progress toward accomplishment of the CREATE outcomes, as well as skill development. That is, the homework problems are not template problems. Each problem has a unique contribution to make to a student's gain in skills and understanding. Students should expect to do all of the homework problems.
Assessment	Most students appreciate the opportunity to show what they know in a variety of ways. For this reason we encourage a variety of assessments. In each lesson, students are encouraged to self-assess by completing the activities, the Wrap-Up boxes and the homework. Assessment ideas for instructors include quizzes, projects, research activities, writing assignments as well as tests.